Like the case of many other practical and realistic potentials, the relevant Schrödinger equation with centrifugal term can not be solved analytically for eigenvalues and eigenfunctions. This has lead to the development of a number of theoretical methodologies of approximation to the centrifugal term in both non-relativistic and relativistic case. Some of the prominent ones may be mentioned. The authors in [1]} have discussed the exact solvability problem via an \(SO(2,2)\)  symmetry algebra. The eigenvalues and eigenfunctions for \(\ell =0\)  states were studied by an algebraic method [2]}. Approximate analytical solutions for rotating DF potential for arbitrary \(n, \ell \)  quantum numbers were given in terms of generalized hyper-geometric functions \(_2F_1(a,b;c;z)\)  [3]}. An improved approximation scheme for the centrifugal term, along with a super-symmetric shape invariance approach was employed in [4]}; analytical solution for Dirac equation has been presented with latter approach [5]}. Solutions of Klein-Gordon equation with spinless particle for \(\ell \ne 0\)  states were considered in [6]}. A Pekeris approximation for centrifugal term and a Nikiforov-Uvarov (NU) method was employed for Dirac, Klein-Gordon and Schrödinger equation [7]}, [8]}. Some other methods include a numerical generalized pseudospectral (GPS) scheme [9]}, exact quantization rule [10]}, [11]}, a Feynman path integral formalism for D-dimensional problem [12]}, etc. A comparative analysis for the performance of Morse, Manning-Rosen, Schlöberg and DF potential in the context of diatomic molecules has been offered in [13]}.
